if the radius of the base of cylinder is halved and the height remains the same, then the ratio of the new volume to that of original volume of the cylinder is_________.
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If the radius of the base of a cylinder is halved, keeping the height the same, what is the ratio of the area of the reduced cylinder and the original one?
Your question isn't complete, since you didn't mention the ratio of area or volume. Well I'll calculate for both the the cases here.
Let old radius = r1
New radius = r2 = r1/2 —(1)
Height of both (reduced and original cylinder) = h
Since volume of cylinder = πr²h
Therefore, ratio of reduced to original cylinder volume = r1²/r2² (since height is same in both and thus cancelled out)
= r1²/(r1/2)² = 4 (from equation 1)
Similarly CSA of cylinder = 2πrh
Therefore, ratio of reduced to original cylinder area= r1/r2
=r1/(r1/2) = 2
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